Darbo type best proximity point (pair) results using measure of noncompactness with application

Abstract

. Primarily this work intends to investigate the existence of best proximity points (pairs) for new classes of cyclic (noncyclic) mappings via simulation functions and measure of noncompact-ness. Use of different classes of additional functions make it possible to generalize the contractive inequalities in this work. As an application of the main conclusions, a survey for the existence of optimal solutions of a system of integro-differential equations under some new conditions is presented. As an application of our existence results, we establish the existence of a solution for the following system of integro-differential equations